IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v121y2014icp164-174.html
   My bibliography  Save this article

An effective approximation for variance-based global sensitivity analysis

Author

Listed:
  • Zhang, Xufang
  • Pandey, Mahesh D.

Abstract

The paper presents a fairly efficient approximation for the computation of variance-based sensitivity measures associated with a general, n-dimensional function of random variables. The proposed approach is based on a multiplicative version of the dimensional reduction method (M-DRM), in which a given complex function is approximated by a product of low dimensional functions. Together with the Gaussian quadrature, the use of M-DRM significantly reduces the computation effort associated with global sensitivity analysis. An important and practical benefit of the M-DRM is the algebraic simplicity and closed-form nature of sensitivity coefficient formulas. Several examples are presented to show that the M-DRM method is as accurate as results obtained from simulations and other approximations reported in the literature.

Suggested Citation

  • Zhang, Xufang & Pandey, Mahesh D., 2014. "An effective approximation for variance-based global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 164-174.
    • Handle: RePEc:eee:reensy:v:121:y:2014:i:c:p:164-174
    DOI: 10.1016/j.ress.2013.07.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832013002202
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2013.07.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Blatman, Géraud & Sudret, Bruno, 2010. "Efficient computation of global sensitivity indices using sparse polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1216-1229.
    2. Tarantola, S. & Gatelli, D. & Mara, T.A., 2006. "Random balance designs for the estimation of first order global sensitivity indices," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 717-727.
    3. Marco Ratto, 2008. "Analysing DSGE Models with Global Sensitivity Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 115-139, March.
    4. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    5. Jeremy E. Oakley & Anthony O'Hagan, 2004. "Probabilistic sensitivity analysis of complex models: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 751-769, August.
    6. Rahman, Sharif, 2011. "Global sensitivity analysis by polynomial dimensional decomposition," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 825-837.
    7. Castillo, Enrique & Mínguez, Roberto & Castillo, Carmen, 2008. "Sensitivity analysis in optimization and reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1788-1800.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jung, WoongHee & Taflanidis, Alexandros A., 2023. "Efficient global sensitivity analysis for high-dimensional outputs combining data-driven probability models and dimensionality reduction," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    2. Wei, Pengfei & Song, Jingwen & Lu, Zhenzhou & Yue, Zhufeng, 2016. "Time-dependent reliability sensitivity analysis of motion mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 107-120.
    3. Wang, Zhenqiang & Jia, Gaofeng, 2023. "Extended sample-based approach for efficient sensitivity analysis of group of random variables," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    4. Wang, Lei & Zhang, Xufang & Zhou, Yangjunjian, 2018. "An effective approach for kinematic reliability analysis of steering mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 62-76.
    5. Sudret, B. & Mai, C.V., 2015. "Computing derivative-based global sensitivity measures using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 241-250.
    6. Yun, Wanying & Lu, Zhenzhou & Feng, Kaixuan & Li, Luyi, 2019. "An elaborate algorithm for analyzing the Borgonovo moment-independent sensitivity by replacing the probability density function estimation with the probability estimation," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 99-108.
    7. Cheng, Lei & Lu, Zhenzhou & Zhang, Leigang, 2015. "Application of Rejection Sampling based methodology to variance based parametric sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 9-18.
    8. Wu, Zeping & Wang, Wenjie & Wang, Donghui & Zhao, Kun & Zhang, Weihua, 2019. "Global sensitivity analysis using orthogonal augmented radial basis function," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 291-302.
    9. Wu, Zeping & Wang, Donghui & Okolo N, Patrick & Hu, Fan & Zhang, Weihua, 2016. "Global sensitivity analysis using a Gaussian Radial Basis Function metamodel," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 171-179.
    10. Qyyum, Muhammad Abdul & Duong, Pham Luu Trung & Minh, Le Quang & Lee, Sanggyu & Lee, Moonyong, 2019. "Dual mixed refrigerant LNG process: Uncertainty quantification and dimensional reduction sensitivity analysis," Applied Energy, Elsevier, vol. 250(C), pages 1446-1456.
    11. Li, Chenzhao & Mahadevan, Sankaran, 2016. "An efficient modularized sample-based method to estimate the first-order Sobol׳ index," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 110-121.
    12. Qian Liu & Xufang Zhang & Xianzhen Huang, 2019. "A sparse surrogate model for structural reliability analysis based on the generalized polynomial chaos expansion," Journal of Risk and Reliability, , vol. 233(3), pages 487-502, June.
    13. Zhang, Xufang & Wang, Lei & Sørensen, John Dalsgaard, 2019. "REIF: A novel active-learning function toward adaptive Kriging surrogate models for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 440-454.
    14. Konakli, Katerina & Sudret, Bruno, 2016. "Global sensitivity analysis using low-rank tensor approximations," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 64-83.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhai, Qingqing & Yang, Jun & Zhao, Yu, 2014. "Space-partition method for the variance-based sensitivity analysis: Optimal partition scheme and comparative study," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 66-82.
    2. Chen, Xin & Molina-Cristóbal, Arturo & Guenov, Marin D. & Riaz, Atif, 2019. "Efficient method for variance-based sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 97-115.
    3. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Variable importance analysis: A comprehensive review," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 399-432.
    4. Lambert, Romain S.C. & Lemke, Frank & Kucherenko, Sergei S. & Song, Shufang & Shah, Nilay, 2016. "Global sensitivity analysis using sparse high dimensional model representations generated by the group method of data handling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 42-54.
    5. Deman, G. & Konakli, K. & Sudret, B. & Kerrou, J. & Perrochet, P. & Benabderrahmane, H., 2016. "Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in a multi-layered hydrogeological model," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 156-169.
    6. Pronzato, Luc, 2019. "Sensitivity analysis via Karhunen–Loève expansion of a random field model: Estimation of Sobol’ indices and experimental design," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 93-109.
    7. Touzani, Samir & Busby, Daniel, 2013. "Smoothing spline analysis of variance approach for global sensitivity analysis of computer codes," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 67-81.
    8. Wu, Zeping & Wang, Donghui & Okolo N, Patrick & Hu, Fan & Zhang, Weihua, 2016. "Global sensitivity analysis using a Gaussian Radial Basis Function metamodel," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 171-179.
    9. Mara, Thierry A. & Tarantola, Stefano, 2012. "Variance-based sensitivity indices for models with dependent inputs," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 115-121.
    10. Dubreuil, S. & Berveiller, M. & Petitjean, F. & Salaün, M., 2014. "Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 263-275.
    11. Sudret, B. & Mai, C.V., 2015. "Computing derivative-based global sensitivity measures using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 241-250.
    12. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    13. Cremona, Marzia A. & Liu, Binbin & Hu, Yang & Bruni, Stefano & Lewis, Roger, 2016. "Predicting railway wheel wear under uncertainty of wear coefficient, using universal kriging," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 49-59.
    14. Rahman, Sharif, 2011. "Global sensitivity analysis by polynomial dimensional decomposition," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 825-837.
    15. Haro Sandoval, Eduardo & Anstett-Collin, Floriane & Basset, Michel, 2012. "Sensitivity study of dynamic systems using polynomial chaos," Reliability Engineering and System Safety, Elsevier, vol. 104(C), pages 15-26.
    16. Plischke, Elmar & Borgonovo, Emanuele & Smith, Curtis L., 2013. "Global sensitivity measures from given data," European Journal of Operational Research, Elsevier, vol. 226(3), pages 536-550.
    17. Girard, Sylvain & Romary, Thomas & Favennec, Jean-Melaine & Stabat, Pascal & Wackernagel, Hans, 2013. "Sensitivity analysis and dimension reduction of a steam generator model for clogging diagnosis," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 143-153.
    18. Becker, William, 2020. "Metafunctions for benchmarking in sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    19. Li, Min & Wang, Ruo-Qian & Jia, Gaofeng, 2020. "Efficient dimension reduction and surrogate-based sensitivity analysis for expensive models with high-dimensional outputs," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    20. Kapusuzoglu, Berkcan & Mahadevan, Sankaran, 2021. "Information fusion and machine learning for sensitivity analysis using physics knowledge and experimental data," Reliability Engineering and System Safety, Elsevier, vol. 214(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:121:y:2014:i:c:p:164-174. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.